Method of designing internally ridged heat transfer tube for optimum performance

ABSTRACT

Metal heat transfer tube has a single start helical ridge on its inner surface which conforms to a range of values of a disclosed equation relating the height of the ridge to its pitch and to the inner diameter of the tube. A method of designing a tube for maximum performance is also disclosed. The improved tube provides especially good results in systems, such as steam condensation systems, wherein a single phase fluid is carried by the tube.

United States Patent Withers, Jr. et al.

METHOD OF DESIGNING INTERNALLY RIDGED HEAT TRANSFER TUBE FOR OPTIMUM PERFORMANCE Inventors: James G. Withers, Jr.; Edward P. Habdas; Michael W. Jurmo, all of Dearborn, Mich.

Universal Oil Products Company, Des Plaines, 111.

Filed: June 29, 1973 Appl. No.: 375,242

Related US. Application Data Division of Ser. No. 232,57l,'March 7, 1972, Pat. No. 3,779,312.

Assignee:

US. Cl. 72/367, 29/l57.3 AH Int. Cl B2ld 53/06 Field of Search 72/78, 367; 165/179, 184;

References Cited UNITED STATES PATENTS 10/1971 Ford 165/179 FOREIGN PATENTS OR APPLlCATlONS 2,009,762 0/1970 France 165/184 860,510 0/1961 Great Britain 72/367 Primary ExaminerL0well A. Larson Attorney, Agent, or Firm-James R. Hoatson, J r.;

Barry L. Clark; William H. Page, 11

[57] ABSTRACT Metal heat transfer tube has a single start helical ridge on its inner surface which conforms to a range of values of a disclosed equation relating the height of the ridge to its pitch and to the inner diameter of the tube. A method of designing a tube for maximum performance is also disclosed. The improved tube provides especially good results in systems, such as steam condensation systems, wherein a single phase fluid is carried by the tube.

2 Claims, 9 Drawing Figures Pmmmum 1 51914 SHEET 10! 2 N Smut mxam x This is a division of application Ser. No. 232,571, filed Mar. 7, 1972, now U.S. Pat. No. 3,779,312. 7

BACKGROUND OF THE INVENTION This invention relates to metal tubing for heat trans- I fer purposes and particularly to such tubing wherein a, special configuration is given to the inner surface to improve its performance.

As explained at some length in British Pat. No. 1,230,196, U.S. Pat. No. 3,612,175, and-especially in U.S. Pat. No. 3,217,799, substantial improvements in heat transfer over plain tubing-can'be achieved by providing special configurations on the inner and/or outer surfaces of tubes. Where the tubing is'to be used in a steam condensation apparatus where a'single phase fluid such as water is on the inside of the tube, it has been found that the major modification which can be made to a plain tube to increaseits overall heat transfer efficiency is one wherein theinterior surfaceis modified. The objective of the surface modification-is to increase heat transfer by corrugating the inner surface to promote fluid turbulence without, at the same time, providing such an increase in the resistance of flow through the tube as to nullify the overall efficiency thereof.

In order to enable comparisons of the tubeside heat transfer performance of different tubes having different internal configurations, the following specialized form of the Sieder-Tate equation may be used:

i/k C, /r (em WM) where h,=inside coefficient of heat transfer, Btu/hrsq ftF constant, dimentransfer coefficient constantf -C, for the particular tube can be determined by means of a modified Wilson plot technique as described at pages] 930 of Industrial Engineering Chem vv istry Process Design and Development, Vol.10, No; l," 1971 ,inan article entitled Steam: Condensing on-Ver-. tical Rows of Horizontal Corrugated And Plain Tubes by J.G."Withers and EH. Young. Although it is generally. desirable to design a tube so that C, is a maximum, there are many instances where one might'desire that C, be of a lower but predetermined value. This latter situation could prevail in the case where allowable pressure drop is severely restricted. Another desirable design feature is to have the corrugated section of the tube have a diameter equal to the diameter ofthe tube ends since a tube will exhibit less friction loss and pressure drop if its corrugated portion has a diameter as large as the tube ends rather than a smaller one.

. 2 In view of the many variables that affect the heat transfer and pressure drop properties of a tube it would be highly desirable to be able'to predict the performance of 'a' particulartube configuration and to be able to predict the configuration which will provide the maximum performance. I

SUMMARY It is an object of this invention to providea single helix metal heat transfer tube having an internal configuration which will provide maximum heat transfer performance. r

It is another object of this invention to provide a means for enabling one to predict theheat transfer performance of the inside surface'of'a tube.

These and other objects are attained by the metal heat transfer tube of the present invention which includes a single start helical ridge on its inner surface.

The function of the ridge is to perturb the liquid flowing' in the tube so that'the liquid can not build up boundary layersjalong the tube wall which would inhibit the transfer of heat from the fluid to the tube wall.

Although the prior art has intimated some of the significant geometrical considerations which affect heat transfer performance, it has failed to relate the geometrical characteristics in away that the response of the heat transfer coefficient C, to variations in geometrical considerations will be predictable. Rodgers U.S. Pat. No. 3,217,799 singles out the ratio'of the axial spacing dimension between adjacent ridges to theridge height dimension as .the significant parameter. Al-

though this relationship is an important consideration, it is-not sufficiently specificto narrow down the most favorable tube design insuch a manner that tube 'performance could be predicted or maximized.

After thoroughly studyingdata from many tubes we have found that there is a geometrical parameter that correlates well with c, This parameter is a dimensionless severity parameter, (b, which involves ridgeheight (e pitch (p) and inside diameter (d,),.in sucha way that: v

many different singlestart helical'ridged can provide'any des'iredvalue of C, up to the maximum and down to that for plain tube. Althoughthe "C, vs 4) correlation has been found to hold true for the =vastma jority'of tubes-studied, it has been noted that in a few of the tubes'the ridge cap dimensions of therhelica'l ridge have been found to be critical in that the measured value of C,- for these vfew tubes did not correspond to the 'value predicted by the C, vs 111' correlation curve.

' Fortunately, this situation-can be resolved by. means of a reinforcing criterion involving a parameter x, which is defined as:

x ety/d,

ter of the tube. A plot of C, vs x has been made which ation; and

indicates that the maximum value of C, corresponds to the extreme maximum value of x. Althoughthe X correlation is not as uniform as the d) correlation, it does seem topredict C, within lOpercent of its measured value. If both the x and correlation curves are used whenever the 4) of a particular single start helically ridged tube exceeds 0.25 X 10 and the lower value-of C,- predicted by the two correlation curves is selected, one can predict with a high degree of accuracy the intube heat transfer performance for turbulent flow of single phase fluid inside the particular tube. For values of below 0.25 X there is no need to use the C, vs X correlator. An alternative procedure to avoid the necessity of using the C, vs x correlation for values of (1) above 0.25 X 10 would be to simply avoid values of t below 0.085 inches since the defect in the C vs d correlation was found to occur only at low values of ridge cap thickness.

An upper limit of 0.365 X 10 for the severity factor is very desirable since beyond this value the value of C, drops off while the friction factor, a direct indicator of pressure drop, increases. Values of d greater than 0.365 X 10 should only be considered for singlephase turbulent intube flow when the controlling thermal resistance is associated with the external surface, and a severely contoured external surface is justified by its improvement contribution, and the internal configuration is incidental to that of theexternal surface of the tube. Although the correlation of C, vs 4) seems to hold true down to a value of 0 where the tube inner surface would be plain, an arbitrary lower limit of d) 0.1 X 10 has been set since the improvement in-the value of C, over that of a plain tube .for lower values of d) is relatively minor.

BRIEF DESCRIPTION THE DRAWINGS FIG. 1 is a partially sectioned side plan view of a plain ended corrugated tube; I

FIG. 2 is an enlarged sectional view of a portion of the corrugated tube section in FIG. 1;

FIG. 3 is a fragmentary sectional view similar to FIG. 2 but showing a modified corrugation shape;

FIG. 4 is a graph illustrating the heat transfer performance of a plurality of single-helix internal-ridged tubes which plots the Sieder-Tate-Equation Constant,

C, as a function of the Severity Parameter qS;

FIG. 5 is a graph illustrating the heat transfer performance of a plurality of single-helix internal-ridged tubes which plots the Sieder-Tate-Equation Constant, C,, in relation to a function, which includes the ridge cap dimensions of the tube; a

FIG. 6 is a graph illustrating theheattransfer performance of single-helix, internal-ridged tubes, expressed as an improvement ratio over-a plain tube; 1

FIG. 7 is a graph illustrating the Pressure Drop characteristics of single-helix internal-ridged tubes taken at an arbitrary. reference Reynolds Number equal ot 35,000 as a function of Severity Parameter, 4:;

FIG, 8 is a graph illustrating the effect of helix pitch on outside tube diameter when internal single-start he lical ridges are formed by an external corrugating oper- FIG. 9 is a graph illustrating a correlation of helix pitch required for a uniform diameter corrugated tube with the product of the outside diameter and the wall thickness.

. DESCRIPTION OF THE PREFERRED EMBODIMENT FIG. 1 shows a corrugated tube indicated generally at 10 having a plain end 12 and a corrugated section 14. The outerdiameter A of the plain end 12 is preferably equal to or very slightly greater than the outer diameter (T) of the corrugated section 14 while the plain end wall thickness E is equal to the corrugated section wall thickness CF. The distance on between identical points on adjacent internal ridges produced by the corrugations is defined as the pitch p.

In the enlargement of the corrugated section 14 shown in FIG. 2, one can see that the internal corrugations comprise ridge portions indicated generally at 20 and connecting portions indicated generally at 22. The ridge portion 20 is generally convex toward the inside of the tube while the connecting portion 22 is generally concave. The portions 20 and 22 join each other smoothly at points of inflection 26 where the ridge arc 20' and the connecting arc 22 have a common tangent. The convex curved portion 27 of the ridge 20 between the points 26 is termed the ridge cap. The ridge cap has a width between points 26, 26 defined as t and a height y" between its crest 28 and points 26. The ridge height e" is the radial distance between ridge crest 28 and the outermost point 30 on the inner surface of connecting portion 22. The internal diameter d, is the diametral distance between points 30 on opposite sides of the tube. The pitch, p, is the distance between any pair of identical points on adjacent ridges 20, such as the points 28.

FIG. 3 illustrates a modification of the tube shown in FIGS. 1 and 2 in that conecting portions 122 are altered in shape as compared to the concave connecting portions 22 of FIG. 2. The connecting portion 122 is flat over a portion 34 of its length. The outer surface of the tube is broken away in Fig. to illustrate the fact that the tube could have a number of different outer surface configurations other than the shape shown in FIG. 2. Since our invention is concerned with improving the tube side heat transfer properties, there is no need to discuss particular external shapes since these will depend on the external heat transfer conditions.

FIG. 4 is a plot of the data derived from testing a plain tube and many single-helix internally ridged tubes using the modified Wilson plot technique previously referenced to determine the value of the Sieder-Tate Equation constant C,. The abcissa of the plot is the severity parameter which is equal to e p d, where e is the depth of the corrugations (FIG. 2), p is the pitch and d, is the internal diameter. The parameter d) is defined as a severity parameter since it is strongly dependent on the ridge height or severity of the corrugations. From the curve 36 it can be seen that C, reaches a peak value when 0.365 X 10f and then drops offas increases. The right hand portion of the curve 36, represents several prior art tubes. Point 38 represents the l in. tube and point 40 represents the n in. tube disas 1.2 in. and the internal diameter d, any value up to about 3 inches.

Although the severity parameter 4) shows an an excellent correlation between tube geometry and the Sieder-TateConstant C, which makes it most easy to design a tube by choosing e, p and d, to provide the iiecessary value of (b for the value of C, desired, the correlation (curve 36) was shown not to hold for a few tubes as evidenced by points 38, 44 and 46 in FIG. 4. These non-conforming tubes proved to provide lower values of C, for their particular values of than would be predicted by the curve 36 of FIG. 4. Fortunately, was found that the tubes which failed to fall on the curve had rather critical ridge cap dimensions. By avoiding tubes with a ridge cap width 1 of less than 0.85 in., the designer can insure that the correlation curve 36 plotted in FIG. 4 will hold. Alternately, another parameter which is, in part, a'furiction of the ridge cap dimensions can be used to predict the value of C This parameter is termed x and is equal to e t y/d, where is the ridge height, t is the width of the ridge cap and d, is the internal diameter. As can be seen in FIG. 5, there is a fairly good correlation between C, and x in that C, increases as x increases. The C, vs curve 48 of FIG. 5 need not be considered for tubes having values of qb which are less than 0.25 X- When (I) is greater than 0.25 X 10*, both the d) correlation curve 36 of FIG. 4 and the correlation curve 48 of FIG. 5 should be considered with the lower value of C, being considered to be the more accurate. 4

FIG. 6 is a plot similar to FIG. 4 except that it relates .6 eter and wall thickness by arbitrarily selecting a given corrugation depth, corrugating the tube at various helix 1 angles, and measuring the resulting outer diameter and corresponding pitch for each of the helix angles.' By connecting the test points witha curve as shown in FIG.

8, the pitch required to provide a uniform diameter can be readily determined.

FIG. 9 is a graph illustrating the helical pitch required to obtain a uniform diameter corrugated tube for any particular product of the tube outside diameter times its wall thickness. The particular correlation curve 60 shown was determined from data derived from a given tube material (90-10 cupronickel) and given groove depth (.032 in.) where the tube was corrugated in a single helix sytle by apparatus such as shown in Anderson US. Pat. No. 3,128,821. A family of such curves could be determined for other tubematerials and groove depths. The correlation is possible since experiments have shown that there exists a certain helix pitch, (p),, which will yield a uniform diameter product in the sense that the maximum projected outer diameter of the corrugated section is essentially equal to the outby curve '50, the improvement ratio over plain tube [C1/ (C,)p] to the (b parameter. This alternative method of displaying the C, vs d) correlation isuseful in comparing results from different laboratories since the base value, (C,)p, for plain tube may varysomewhat among different test setups.

FIG. 7 illustrates a correlation of pressure drop characteristics of single-helix, internal-ridge tubes as a function of the severity parameter (1) where the pressure drop is expressed as Friction Factor, f, at a reference Reynolds number of 35,000. It is commonly understood that the friction factor,f,- is a direct index of pressure drop per unit length of tube, as long as one compares tubes of a given diameter at the same Reyonlds number. Since it is evident from the curve 56 of FIG. 7 that pressure drop increases significantly with increases in the severity parameter (1:, it is desirable that tubes be configured so that not be permitted to increase beyond the optimum vvalue of 0.365 X 10' Such an increase in 4) would not only result in a lower value of C, but would also cause a presumably undesirable increase in pressure drop. In certain instances, design limitations on length, pressure drop, diameter, etc.

could render appropriate the selection of 11 below 0.365 X 10 even though entailing a lower value of C FIG. 8 illustrates the effect of the helix pitch, p, on the outside diameter of a corrugated tube when internal single-start helical ridges are formed by an external corrugating operation of the type shown-in Anderson U.S; Pat. No. 3,l28',82l.' The curve 58 slflvs that by varying the pitch p, the outside diameter CD (FIG. 2) of the corrugated section 14 can be varied so as to either decrease or increase relative to the outside diameter A B of the uncorrugated section 12 of the tube 10. The curve 58 is obtained for any particular alloy, diamside diameter of the plain starting tube. In order to apply the teachings of the invention to the design of a single start, internally grooved tube where it is desired to achieve maximum heat transfer between a single phase liquid in the tube and the tube surface, the following procedures should be followed:

1'. Select a material, outside diameter, and wall thickness which will provide the necessary corrosion resistance, strength and cost, for example, for the intended use. I 2. Assuming that a uniform diameter product is desired, multiply the outside diameter times the wall thickness and read the corresponding pitch from a curve suchas curve in FIG. 9. If the curve 60 hasnot been determined for the particular material and corrugation depth, the proper helix pitch for various groove depths may be determined by trial and'error by selecting various helix angles and groove depths until the diameter remains constant. This should be done until several combinations are known which will provide a constant outside diameter.

3. Using the equation, 4) e /Pd, 0.365 X 10*, various values of p should be tried until a resulting value of e is found which is identical to the groove depth which must be used with the particular value of p to achieve-a constant diameter. 7

If it is desired to design a tube so that C, isa particular value less than its maximum, the value of 45 corresponding to the desired value of C, can be found on curve 36 in FIG. 4, The'values of p,. and e which should be used can then be determined as set forth in the preceding example. When designing for either a maximum or a particular C,, the designer should also check curve 48 in FIG. 5 when d) is between 0.25-0.365 X 10 and t is less than 0.085 in. to be certain that a'C, as high as predicted by curve 36 will be obtained.

The teachings of the present invention relative to designing tubesfor maximum internal heat transfer are 1 applicable to any of the commom tube materials such as cuprous alloys, titanium, stainlesssteel, carbon steel and aluminum and are independent of outside diameter and the outer configuration of the tube.

Of all the tubes used to establish the various correlations previously set forth herein, one seemed to exactly correspond to the predicted criteria for a single-helix, internally grooved tube which would have a maximum value of C This tube was made of 90-10 Cupronickel and had the following dimensions: Outer Diameter (plain end) 1.250 inches; Outer Diameter (corrugated end) 1.249 inches Wall .050 inches; d 1.149 inches; e inches =0.046 inches; p =0.505 inches; t 0.120 inches; y 0.0l inches; :11 0.365 X X=O.48 X 10- infi; C,-=0.0693: Ci/(Ci) =2.62.

We claim as our invention:

1. A method of making a heat transfer tube having a single start helical ridge on its internal surface so that a single phase fluid flowing in the tube will have maximum heat transfer with the tube wall, comprising the ter, 11;, the depth, e of such corrugations on the interior surface being selected so that e /Pd, will be euqal to about 0.365 X 10*2.

2. A method of making a heat transfer tube having a single start helical ridge on its internal surface so that a single phase fluid flowing in the tube will have a selected amount of heat transfer with the internal surface between the maximum possible for such a ridged tube and the minimum provided by a plain tube, comprising the steps of:

a. selecting a plain metal tube of a suitable material,

diameter and wall thickness;

b. corrugating at least a portion of the interior of said tube at a helix angle and depth so as to define an internal helical groove having a pitch p, and an internal diameter d,-" such that e /Pd; will have a value in the range 00.365 X 10 generally proportional to the amount of heat transfer desired between that for a plain tube and the maximum possible for such a ridged tube. 

1. A method of making a heat transfer tube haVing a single start helical ridge on its internal surface so that a single phase fluid flowing in the tube will have maximum heat transfer with the tube wall, comprising the steps of: a. selecting a plain metal tube of a suitable material diameter and wall thickness; b. corrugating at least a portion of said tube at a helix angle and depth which will cause the outer diameter of the corrugated portion to be approximately equal to the initial outer diameter of the tube and define the helical pitch ''''p'''' and the internal diameter, ''''di,'''' the depth, ''''e'''' of such corrugations on the interior surface being selected so that e2/Pdi will be euqal to about 0.365 X 10
 2. 2. A method of making a heat transfer tube having a single start helical ridge on its internal surface so that a single phase fluid flowing in the tube will have a selected amount of heat transfer with the internal surface between the maximum possible for such a ridged tube and the minimum provided by a plain tube, comprising the steps of: a. selecting a plain metal tube of a suitable material, diameter and wall thickness; b. corrugating at least a portion of the interior of said tube at a helix angle and depth so as to define an internal helical groove having a pitch ''''p,'''' and an internal diameter ''''di'''' such that e2/Pdi will have a value in the range 0-0.365 X 10 2 generally proportional to the amount of heat transfer desired between that for a plain tube and the maximum possible for such a ridged tube. 